Demonstration of Spread Spectrum Communication through Mathematical Simulation

7/28/2019 Demonstration of Spread Spectrum Communication through Mathematical Simulation

1/52

Demonstration of Spread Spectrum Communication through

Mathematical Simulation

Karthik Uppuluri

University College University of Denver

TELE 4901: Capstone Project

December 9, 2007

______________________________Carl M. Shinn, Jr.Capstone Advisor

______________________________

Thomas J. TierneyAcademic Director of Telecommunications

Upon the Recommendation of the Department:

______________________________James R. Davis

Dean


2/52

Karthik-ii

1 ABSTRACT

This project demonstrates how a direct-sequence spread spectrum

(DSSS) transceiver works under the influence of an Additive White

Gaussian Noise (AWGN) channel. The DSSS system is designed so

that the signal is varied along with the Pseudo-random Noise (PN)

sequence and modulated with Binary Phase Shift Keying (BPSK).

Receiver system is also is designed to get back the original signal

using error correction and BPSK demodulation. The fundamental

components of the DSSS as well as its intermediate signals and their

interaction are made visible in this presentation, which thus serves

as a superior learning/visualization tool.


3/52

Karthik-iii

Table of contents:

Title page.......................................................................................................................... i

ABSTRACT ....................................................................................................................... ii

1. INTRODUCTION .......................................................................................................... 5

2. SPREAD SPECTRUM AND ITS TECHNIQUES ........................................................ 6

3. DIRECT SEQUENCE SPREAD SPECTRUM (DSSS)............................................... 10

4. DSSS TRANSMITTER................................................................................................ 11

4.1. Transmitter Scope Results ..................................................................................... 12

5. TRANSMITTER COMPONENTS AND RESULTS .................................................. 14

5.1. Random Integer Generator..................................................................................... 14

5.2. Unipolar to Bipolar ................................................................................................ 16

5.3. PN-Sequence Generator......................................................................................... 18

5.4. Spreader ................................................................................................................. 22

5.5. Bipolar to Unipolar Converter ............................................................................... 24

5.6. Band Pass Shift Keying Modulator........................................................................ 24

5.7. Normalized Gain.................................................................................................... 30

6. AWGN CHANNEL COMPONENTS.......................................................................... 31

7. DSSS RECEIVER ........................................................................................................ 34

7.1 Receiver Scope results.35

8. RECEIVER COMPONENTS AND RESULTS........................................................... 37

8.1. M-ary PSK Demodulator....................................................................................... 37

8.2. Despreader ............................................................................................................. 40

8.3. Tapped Delay......................................................................................................... 41


4/52

Karthik-iv

8.4. Integrate and Dump................................................................................................ 42

8.5. Error rate calculator ............................................................................................... 45

9. COMPLETE DSSS SYSTEM...................................................................................... 45

10. CONCLUSION........................................................................................................... 48

11. REFERENCES ........................................................................................................... 49

12. APPENDIX................................................................................................................. 50


5/52

Karthik-5

1. INTRODUCTION

The spread spectrum concept originated in the period from 1920 to

1960, which led to the development of spread-spectrum

communication systems (IEEE Trans Communication 1982, 882).

During those times the communication was done using techniques

like FDMA and TDMA, which are vulnerable to attack. The bandwidth

needed is also high for these legacy systems, which was not a

major issue in the military. But those methods were highly insecure

in terms of confidentiality. The spread spectrum technique was

introduced in the 1920s, which brought a drastic change in the

communication world. These spread spectrumsystems were used

mainly for the military purpose so that signal can be sent securely

without jamming. The main advantage of this technique is that

spread signal appears like a random noise, which is difficult to

demodulate by anybody other than the authorized receiver. During

that time, lot of research was going to change the wired telephone

systems to wireless, resulting in major breakthroughs in the

communication world. All these techniques were applied in wireless

technology that changed the face of the corporate world.

There are two types of spread spectrum techniques that are used

widely: Direct Sequence Spread Spectrum (DSSS) and Frequency


6/52

Karthik-6

Hopping Spread Spectrum (FHSS) technique. Spread Spectrum

systems have found their use in the corporate world primarily for

wireless digital communication. Code division multiple access

(CDMA) is one of the best applications of spread spectrum system in

this corporate world. CDMA mainly uses DSSS; for simplicity sake it

is explained clearly in the project for single user. Bluetooth is the

major application for Frequency Hopping Spread spectrum

technique. A DSSS transceiver model is developed in the project.

Some basic concepts that are very important for these technologies

are also discussed in succeeding sections.

2. SPREAD SPECTRUM AND ITS TECHNIQUES

The general model of Spread spectrum Technique is shown in Figure

1. It shows that the data signal to be transmitted is multiplied by

the spreading code (This is the general case and it can be any kind

of sequence.). Then the spread signal is transmitted. The receiving

side acquires the transmitted signal, which is then multiplied by a

spreading code again, so that the original signal is recovered. It can

be observed that the desired signal gets multiplied twice but the

interference gets multiplied only once, which is a huge advantage

and will reduce the interference. (Simon, et al. 1994)


7/52

Karthik-7

Figure 1: Basic model of spread spectrum technique (Simon, et al.

1994).

The main property of the spreading signal is the bandwidth

expansion factor (Be=Width/Datarate), which is much greater than

unity, which means the redundancy involved in the spread signal

can easily overcome the interference. The basic block diagram

referenced in the project is shown in Figure 2.

Spreading Code Signal Spreading Code Signal

Filter

Recovered

Signal


8/52

Karthik-8

Figure 2: Block diagram showing the basic spread spectrum digital

communication System (Proakis 2000).

The project is designed from above basic model using

MATLAB/Simulink. In the above block diagram the digital signal is

inserted at the transmitter end and received at the receiver end

after proper manipulation. During this transmission the signal goes

through a modulator and a demodulator for mixing with patterns

created by pseudorandom number (PN) generators. Synchronization

of the PN-generators is important for the receiver side to

demodulate. The PN-generator is used along with a Phase Shift

Channel Encoder Modulator

Pseudorandom

PatternGenerator

PseudorandomPattern

Generator

De-ModulatorChannel Decoder

C

H

A

NNE

L


9/52

Karthik-9

Keying (PSK) modulator and demodulator to change the phase of

the signal.

The above discussion applies only for a single user as mentioned

above due to the complexities associated with designing a system

for multiple users. The encoding and decoding techniques are same

for both. They can be distinguished from each other by

superimposing a differential pseudorandom pattern called a code for

the transmitted signal. (Simon, et al. 1994)

Reducing the transmitted power of the spread signal along its whole

bandwidth can also hide the signal. This type of signal is called a

Low Probability of Intercept (LPI) signal. Superimposing a

pseudorandom code, which is the kind of technique that has been

used in the project, attains the privacy of the message. (Ziemer and

Peterson 1985)

This concludes the discussion of different ways of transmitting a

signal. The next part explains the particular simulation of a DSSS

system.


10/52

Karthik-10

3. DIRECT SEQUENCE SPREAD SPECTRUM (DSSS)

This is the spreading technique that is mainly used in the CDMA

transmission system. With DSSS, multiple bits in the transmitted

signal represent each bit in the original signal, using a spreading

code .The spreading code spreads the signal across a wide

frequency band in direct proportion to the number of bits used.

Therefore, a ten-bit spreading code spreads the signal across a

frequency band that is ten times greater than a one-bit spreading

code. When the signal spreads ten times greater, the energy will

vary. Normalized gain is used in the simulations to keep the energy

constant. (Stallings 2004) More information on how a signal is

transmitted and received is clearly explained in Sections 4 through 7

below.

The DSSS model includes these major components:

1. Transmitter

2. Receiver

3. Channel


11/52

Karthik-11

4. DSSS TRANSMITTER

Figure 3 shows the Simulink transmitter design. The input to the

transmitter is given from the random integer generator. This random

integer sequence simulates information generated by a user. The

output from the random integer generator is converted to bipolar

waveform.

Figure 3: Simulink transmitter design.

As the signal needs to be spread, a PN sequence generator is used,

which generates a random binary sequence. The output from the PN


12/52

Karthik-12

sequence generator is also converted to a bipolar waveform from

the unipolar waveform. Now both the information sequence and the

PN-sequence are multiplied, resulting in the spreader signal. The

next stage is modulation where the spread signal is modulated. An

M-ary Phase Shift Keying (M-PSK) modulator is used and the

parameters are set in such a way that it works as a Binary Phase

Shift Keying (BPSK) Modulator. The output of a BPSK modulator is a

sine wave where it changes its phase by 180 degrees. Now the

information is ready for transmission but the energy when spread

will be less than the original signal, so normalized gain is used to

restore the energy of the signal. The output from different blocks is

given to the scope, where the output is plotted. The snapshots of

these results are captured at the same time and are shown in the

following sections.

4.1. Transmitter Scope Results

Figure 4 below shows the outputs from all the blocks on the

transmitter side. The result is discussed in detail in the next section

which explains each block separately.


13/52

Karthik-13

Figure 4: The transmitters output with all the scopes together.


14/52

Karthik-14

5. TRANSMITTER COMPONENTS AND RESULTS

This section discusses the transmitter blocks completely with the

scope results after each block.

5.1. Random Integer Generator

The random integer generator uniformly distributes random integers

in the range (0, M-1), where M is the number of the array.

Assuming the M value is 2, the integers range is (0,1). The random

integer generator is conventional to use as a source.

The following parameters are to be defined for this block and are

selected randomly to get the desired output waveform:

1) M-array number.

2) Initial seed: Vector length seed determines length of output

vector and by default it is set to 37

3) Sample time is chosen as .01sec

4) Samples per frame

These are parameters used for the random integer generator; the

parameter block is pasted from MATLAB/Simulink.


15/52

Karthik-15

Figure 5: Parameter block of Random Integer Generator

Figure 6 is an oscilloscope result that shows the random integer

generator output, generating uniformly distributed random integers

in the range [0, M-1], where M is an M-array number.


16/52

Karthik-16

Figure 6: Random Integer Generator Scope

5.2. Unipolar to Bipolar

The Unipolar to Bipolar Converter block maps the unipolar input

signal to a bipolar output signal. If the input consists of integers

between 0 and M-1, where M is the M-ary number parameter, then

the output consists of integers between -(M-1) and M-1. If M is

even, then the output is odd. For an example if the input is [0; 1; 2;

3], the M-ary number parameter is 4, and the Polarity parameter is

Positive, then the output is [-3; -1; 1; 3]. Changing the Polarity

parameter to Negative changes the output to [3; 1; -1; -3]. Figure

7 shows the parameter settings for the unipolar to bipolar converter.


17/52

Karthik-17

Figure 7: Parameters of Unipolar to Bipolar Converter

Figure 8 shows a scope result with a bipolar output signal. If the

input is from 0 to M-1 integers, then the output consists of integers

(M-1) and (M-1).

Figure 8: Random Unipolar to Bipolar Signal.


18/52

Karthik-18

5.3. PN-Sequence Generator

A pseudo noise (PN) generator creates a pseudo random sequence

to simulate a noise signal. The generated PN sequence is not

completely random, but the PN code is a deterministic periodic

signal that is known to both the transmitter and receiver. (A random

signal cannot be predicted, but its future can be determined

statistically.) PN is called so because its statistical properties are

the same as sampled white noise (Sklar 2001).

The DSSS is simulated using MATLAB/Simulink software and the

block used is a PN-sequence generator. It uses a sequence of shift

registers to generate the sequence as shown in the Figure 9. In

Figure 9, the adder performs the modulo 2 addition. All the registers

that are represented by square boxes get updated every time form

the earlier one.

The generation polynomial can be represented as

1 2

1 2 0....................n n n

n n ng z g z g z g

+ + + +

The leading term is g n and constant term g o.


19/52

Karthik-19

Figure 9: PN Generator Showing shift Registers

In MATLAB/Simulink this can be represented in two ways. The first

is like a vector that lists the coefficients of the polynomial; second

one is like a vector containing the exponents of Z in descending

order of power. The parameters are set and discussed in Figure 10.

gn gn-1 gn-2 g1 g0

o/p


20/52

Karthik-20

Figure 10: Parameters of PN generator

As the scope result shows in Figure 11, the PN sequence generator

generates random sequences.


21/52

Karthik-21

`

Figure 11: PN Sequence Generator

Figure 12 shows the same signal after the unipolar to bipolar

converter. It can be seen that the output now varies from -1 to 1.


22/52

Karthik-22

Figure 12: PN Unipolar to Bipolar Converter.

5.4. Spreader

The spreader is nothing but a multiplier. There are three input

variables in the parameters block shown in Figure 13. The number

of inputs determines how many inputs should be multiplied and also

the multiplication is element wise. By default the sample time is -1.

The spreader multiplies the PN sequence times the data signal that

represents the user signal (voice or data). Figure 14 shows an

example of the spreader output signal.


23/52

Karthik-23

Figure 13: Parameters of the Spreader

Figure 14: Spreader output signal example


24/52

Karthik-24

5.5. Bipolar to Unipolar Converter

Since certain inputs to certain blocks can not be bipolar, this

converter changes from bipolar to unipolar. A typical configuration

is shown in Figure 15.

Figure 15: Parameters of Bipolar to Unipolar Converter

5.6. Band Pass Shift Keying Modulator

Modulation is the process of transforming digital symbols into

waveforms, which can be sent through specific channels. (Sklar

2001)

In this case a desired information signal modulates a sinusoidal

signal called a carrier wave. Since this spread spectrum

communication project is using it fortelecommunication purposes,


25/52

Karthik-25

the carrier is converted to an electro magnetic signal that can be

transmitted by an antenna. To increase the frequency so that a

smaller antenna can be used, a modulator combines the signal with

a carrier.

Other advantages of band pass modulation are multiplexing signals

and minimizing interference. The next section explains digital

modulation as implemented in the project.

An information signal is converted into a sinusoidal wave and a

duration T is referred as digital symbol. Any signal can be varied by

three factors: amplitude, frequency and phase. In Pass Band, all

three factors can be varied in accordance with the information to be

transmitted. (Sklar 2001)

0

0

( ) ( )cos[ ( )]

( )

( )

( )

s t A t t t

t is phase

A t is amplitude

t is Angular Frequency

= +

There are two types of digital modulation techniques, coherent

detection and non-coherent detection. If the receiver utilizes the


26/52

Karthik-26

carrier properties such as the phase, then it is called coherent

detection. During non-coherent detection, the receiving side doesnt

need the carrier. This DSSS simulation uses coherent detection.

In ideal coherent detection there are prototypes available at the

receiver side. These waveforms attempt to duplicate the transmitted

signal in every aspect. During detection, the receiver multiplies and

integrates (correlates) the incoming signal.( Sklar 2001)

For phase shift keying, the general expression can be given as

0

2( ) ( ( ))

0

1,2,.......

i i

ES t Cos t t

Tt T

i M

= +

=

Where the phase term can be represented as

2( )

.

i

it

M

T Symbol duration

E Symbol Energy

=

=

=

In this project Binary Phase Shift Keying (BPSK) is used, where the

signal shifts the phase of the waveform. There are two states of

change either from 0 to 180 or vice versa.Figure 16 shows how the

waveform varies.


27/52

Karthik-27

Figure 16: Figure showing the phase changes. (Stallings 2004)

If the modulating signal has zeros and ones, then there will be a

change in a signals phase during its transmission. This kind of

signal can be represented as vectors on a polar plot. While changing

the complex part to real and imaginary parts in an M-array, the

signal phase relates to m-1 sets. Few blocks have been changed in

the project to represent this kind of signal. These types of signals

are called antipodal signals. The parameter settings of the Binary

PSK modulator are shown in Figure 17 and are explained in order..


28/52

Karthik-28

Figure 17: Parameters of M-ary Phase Shift Keying modulator.

Since the project uses BPSK modulation, M=2. The input type and

constellation parameters are bits and as B stands for binary, the

third parameter is binary. A symbol period of 1/800 has been

selected, resulting in the carrier frequency 2 * Pi * F, which is

approximately 8000. And the final one is the output sample time

which is 1/400,000.


29/52

Karthik-29

Figure 18 shows the result after the BPSK modulator and the

changes in the sine wave are clearly seen.

Figure 18: Scope showing the phase changes after the M-PSK

Modulator.


30/52

Karthik-30

Figure 19: Figure showing the phase changes. (Stallings 2004)

Figure 19 shows the theoretical result and it is exactly same as

Figure 18 from the simulation.

5.7. Normalized Gain

The input bits are spread after passing through the spreader, but

the total energy must remain unchanged. Supposing three bits of

original input are converted to six bits after spreading. Then the

energy in six bits after spreading must be equal to the energy of

three bits in the original message. To keep the energy constant,

normalizing gain is used.


31/52

Karthik-31

Figure 20: Parameters showing the Normalized Gain.

Figure 20 shows a typical normalized gain setting block from

MATLAB/Simulink.

6. AWGN CHANNEL COMPONENTS

This simulation models real world conditions by the linear addition of

white noise with constant spectral density and Gaussian distribution

of amplitude. This simulation channel produces similar results to

those when a real signal comes across thermal noise, short noise

and black body radiation. After the signal is transmitted in the

simulation, it is sent to an AWGN channel that acts like a noisy


32/52

Karthik-32

channel. The output from AWGN channel is the information signal

mixed with noise.

Figure 21: Parameters of AWGN channel

Figure 21 shows the settings for the AWGN channel. Figure 22

shows the signal after it is passed through the addition of noise by

the AWGN channel.


33/52

Karthik-33

Figure 22: AWGN Channel output showing signal with noise added.


34/52

Karthik-34

7. DSSS RECEIVER

Figure 23: Receiver Side Block Diagram

The receiver (whose block diagram is shown in Figure 23) has the

task of recovering the original transmitted signal. First, the noisy

signal is demodulated and changed to a bipolar signal. The signal is

then unbundled by combining it with the PN sequence. When both

the signals are multiplied, the original signal is obtained. Then the


35/52

Karthik-35

signal is sent to the integrate and dump function, which integrates

the input signal in discrete time and sees that it is between the

absolute value of K-integers. The result is sent to dump and resets

itself for next input. The signal is then sent to a zero order hold to

restore the signal properties. At last the signal is again sent to

bipolar to unipolar converter and the output is plotted on the scope.

7.1 Receiver scope results

Figure 24 shows simulated signals at various points in the receiver.

The DSSS function is especially highlighted by comparing the first

(AWGN channel) and last (Received Signal).


36/52

Karthik-36

Figure 24: The Receiver output as one scope.


37/52

Karthik-37

8. RECEIVER COMPONENTS AND RESULTS

This section discusses all of the receiver components and shows the

oscilloscope traces of all output signals after each component.

8.1. M-ary PSK Demodulator

The receiving signal is fed directly into a demodulator where it is

demodulated with the same parameters as that of the modulator. The

parameters that are used are shown in Figure 25. Figure 26 shows

that the demodulation is finished while Figure 27 shows the result

after synchronization.


38/52

Karthik-38

Figure 25: Parameters of M-PSK Demodulator


39/52

Karthik-39

Figure 26: M-PSK Demodulator Pass Band before synchronization.

Figure 27: M-PSK Demodulator Pass Band after synchronization.


40/52

Karthik-40

8.2. Despreader

The despreader is similar to the spreader. In this case the PN

sequence is multiplied by the incoming signal, so that the signal is

decoded completely. Similarly the despreader parameters are

shown in Figure 28. The resulting waveform is shown in Figure 29.

Figure 28: Parameters of Despreader.


41/52

Karthik-41

Figure 29: Despreading Signals.

8.3. Tapped Delay

Before it is fed to the error rate calculator, the signal is delayed. The

Tapped Delay block delays its input by the specified number of

sample periods, and outputs the same signal with this constant

delay.

This block provides a mechanism for discretizing a signal in time, or

resampling the signal at a different rate. The time samples specify

the time between samples with the Sample time parameter. A

value of -1 instructs the block to inherit the number of delays by

backpropagation. Each delay is equivalent to the z-1 discrete-time

operator, which is represented by the Unit Delay block.


42/52

Karthik-42

The Tapped Delay function block (shown in Figure 30) accepts one

scalar input and generates an output for each delay. The input must

be a scalar. Oldest orders the output. So for error rate calculation,

prior to comparison, the input signal is delayed for 1 sample time.

Figure 30: Parameters of Tapped Delay.

8.4. Integrate and Dump

This block integrates the input signal in discrete time and sees that

it is between the absolute value of K-integers. As it resets itself after

certain time, the signal integrates and sends the result to the output

port and clears the internal state for the next time step. Figure 31

shows the parameters of the Integrate and Dump function block.


43/52

Karthik-43

Figure 31: Parameters of Integrate and Dump

Figure 32 shows the Integrate and Dump output and demonstrates

that it integrates the despreaded signal.

Figure 32: Integrate and Dump.


44/52

Karthik-44

The last section to be discussed is the Error Corrector, where the

error is corrected in order to get back the original signal. In Figure

33 are two scope displays taken before and after error correction. It

is easily seen that the received signal is not identical to the

transmitted signal. The reason is that the signal is passed through a

error rate calculator which is set to the incorrect parameters shown

in Figure 34. The appropriate correction is revealed in Section 9

below.

Figure 33: Transmitted signal (above) and received signal (below)

before error correction.


45/52

Karthik-45

8.5. Error rate calculator

Figure 34: Parameters of Error Correction.

9. COMPLETE DSSS SYSTEMThis section discusses in detail the complete DSSS transceiver

designed with the basic blocks. This section summarizes all topics

discussed in the project. BPSK is implemented as the spreading

modulation technique. An ideal BPSK modulation results in

instantaneous phase change of the carrier by 1800.These results

illustrate why the BPSK modulator falls under the coherent systems

category. Figure 35 is the comprehensive block diagram of the

complete DSSS transmitter/receiver link. Resulting transmitted and

received signals created by the simulator are shown in Figure 36.


46/52

Karthik-46

Figure 35: DSSS Simulink Block Diagram

Figure 36 displays the result that the transmitted signal and the

received signal are identical. This indicates that the signal has been

successfully communicated using DSSS technology.


47/52

Karthik-47

Figure 36: Transmitted Signal (above), Received signal (below),

after error correction.


48/52

Karthik-48

10. CONCLUSION

This project provides a tool for understanding spread spectrum

technology and its implementation. A DSSS transceiver is designed

and demonstrated via simulation using a tool called

MATLAB/Simulink. Simulation components used include a basic

BPSK modulator along with a PN generator. Internal signals within

the simulated transmitter and receiver are captured to reveal the

DSSS operation. This project enables convenient exploration of

spread spectrum. The project could also be useful in research by

permitting observation of the results when DSSS parameters and

configurations are changed.


49/52

Karthik-49

11. REFERENCES

Sklar, Bernard.. 2001. Digital communications fundamentals and

applications. New York: Prentice Hall Professional Technical

Reference.

The Mathworks MATLAB and Simulink for technical computing.

https://mathworks.com (Accessed October 10th, 2007)

Proakis, John. 2000. Digital communications. New York: McGraw-Hill

Companies.

Simon, Marvin K., Jim K. Omura, Robert A. Scholtz, and Barry K.

Levitt. 1994. Spread Spectrum Communications Handbook.

New York: McGraw-Hill, Inc.

Stallings, William. 2004. Wireless communications and networks.

New York: Prentice Hall.

Ziemer, Rodger E. and Roger L Peterson. 1985. Digital

Communications and spread spectrum systems. New York:

Prentice Hall.

Scholtz, R. 1982. The origins of spread spectrum communications.

IEEE Trans Communication 882-854


50/52

Karthik-50

12. APPENDIX

LIST OF FIGURES:

FIGURE Name

1 Basic Model of Spread Spectrum Technique

2 Basic Spread Spectrum Digital Communication System

3 Simulink DSSS Transmitter Design

4 DSSS Transmitter Result

5 Random Integer Generator

6 Random Integer Generator Scope

7 Random Unipolar to Bipolar

8 Random Unipolar to Bipolar Scope

9 PN Generator showing Shift Register

10 PN-Sequence Generator

11 PN-Sequence Generator Scope

12 PN-Unipolar to Bipolar Scope

13 Spreader


51/52

Karthik-51

14 Spreader Scope

15 Bipolar to Unipolar

16 Figure Showing the Phase change

17 M-PSK Modulator

18 M-PSK Modulator Scope

19 Figure Showing the Phase change

20 Normalized Gain

21 AWGN Channel

22 AWGN Channel Scope

23 Simulink DSSS Receiver Design

24 DSSS Receiver output Scope

25 M-PSK Demodulator

26 M-PSK Demodulator Scope

27 After Synchronization Scope

28 Despreader

29 Despreader Scope

30 Tapped Delay

31 Integrate and Dump

32 Integrate and Dump Scope


52/52

Karthik-52

33 Tx signal,Rx signal Scope(Before error correction)

34 Integrate and Dump

35 Simulink DSSS Transceiver Design

36 Tx signal,Rx signal Scope(After error correction)

Date post:	03-Apr-2018
Category:	Documents
Upload:	shervinsh
View:	225 times
Download:	0 times

Demonstration of Spread Spectrum Communication through Mathematical Simulation

Documents